I recently had a 16 mo Shiba Inu fall into our hands, and he's a handful and confusing, while also being adorable. Being a first time dog owner, i'm not sure if some of his behavioral issues are because of separation anxiety from his old owner, or if I may be making a mistake in trying to train him.

He is not fixed, but will have the procedure done in the next few days (not sure if that attributes to anything.)Anyways, the issues I am having with him are that he is consistently scratching at doors, walls, and even the floor next to my computer desk, as if he is trying to indicate he wants something. This is confusing for me because we he will already have been fed and taken outside in order to do his business. These behaviors are accompanied by whining, barking, howling, etc.

We have only had him for ~3 weeks, and we allowed him time to adjust for the first week, and have only began attempting to train here in the last 1.5 weeks or so. I understand that there are no "overnight changes" when it comes to training but am curious as to what others think, and what others recommend for demonstrating to him that crying/howling are not the correct ways to indicate he needs something, and that he needs to be patient, and most of all quiet.

Without turning this into a wall of text I can answer any questions pertaining to details I have left out in the comments!

What else do you do to 'entertain' or challenge him? At 16 months they have a lot of energy and need a lot of physical and mental stimulation. He is probably still adjusting to his new home too but if you up the exercise and challenge his brain with some training, games, nose work I think you will start to see some difference.

Yeah, I agree with @Juni here. It sounds like he's bored. Maybe look in to some puzzle type toys for the times you can't interact with him, and teach him fetch for when you can spare some minutes at your desk. We use a handful of small stuffies for playing fetch with Rhyz and hide and seek in the house with Laika (she's really good with names so we've named most of the toys and ask her to go find them, this is a fun game for her).

Sneak in some training sessions to break up the monotony for your dog, too. A couple of short 5 minute sessions throughout the day will help keep them satisfied.

Doesn't really sound like an anxiety thing at all, to be honest. When Rhyz gets bored he'll close the office door and scratch at the floor in front of it.

Based on your description, I don't know if I could confirm a cause for his behavior. I do agree with the previous comments that finding things to keep him busy and burn through some of his young dog energy may help. Does it seem like he's trying to get your attention when he scratches? Or does it seem like a compulsive behavior that he gets pleasure/satisfaction from? Those are things to consider.

Shibas are smart. They can learn quickly if positive training techniques are used. I would try consistently correcting him and redirecting him each and every time he starts to scratch. You don't have to yell or be forceful. Choose a specific sound that you make each time you want to indicate an unwanted behavior. We use "eh-eh!" Use that sound to get his attention, then redirect him to a chew toy, a ball, or something that is appropriate behavior. Then praise him if the scratching stops. If he resumes scratching, tell him "eh-eh!" again - if you need to, gently stop him from scratching (put your hand on his paw gently) and re-direct. Eventually, this should train him that scratching is not good, but his toys, puzzles, chewies are good things to do when he's bored. Does that make sense?